What is 0.45 repeating as a fraction?

Answer 1

0.45 repeated = 5/11

METHOD #1

0.45 repeated = 0.45 + 0.0045 + 0.000045 ...

r = 0.01 [common ratio between each term]

n = 0.45 [beginning term]

As |r|<1

0.45 + 0.0045 + 0.000045 ... forms a limiting sum

Limiting sum = S(n) = n / (1 - r)

= 0.45/(1 - 0.01)

= 0.45/0.99

= 45/99

= 5/11

METHOD #2

Let x = 0.45 repeated

100x = 45.45 repeated

100x - x = 45.454545454545... - 0.454545454545...

99x = 45

x = 45/99

x = 5/11

Answer 2

0.454545...

Let P = 0.454545....

Hence

100P = 45.454545...

Subtract

99P = 45. 0 = 45 ( NB THe recurring decimals to infinity subtract to zero.

99P = 45

P = 45/99

Cancel down by '9'

5/11

The answer!!!!